(CNN) -- Hundreds of Spirit Airlines pilots walked off their jobs on Saturday morning after negotiations over pay with the low-cost carrier hit a stalemate.

The two sides had worked through the night to reach an agreement, but could not resolve their differences.

"Immediately after 5:00 a.m., the Spirit Pilot Master Executive Council, as authorized by our pilots, called for and instituted a lawful strike against our management," said Capt. Sean Creed, head of the Spirit unit of the pilot union, Airline Pilots Association.

The airline canceled all flights for Saturday and, in a message posted on its website, promised passengers a refund or a flight credit.

"Spirit Airlines is continuing to work with our pilot union to reach a fair and equitable agreement that ensures the long-term stability of the company, and allows us to continue offering you the ultra low fares you have come to know and love. In the meantime, as of today, the pilot union has declared a strike," the message said.

It was later taken down.

Spirit pilots have complained that their pay is not proportional to those of their counterparts at other American airlines.

"The strike comes after nearly four years of contract negotiations and numerous attempts by the pilots to find a middle ground with management and avoid a strike," the ALPA said in a statement. "All Spirit pilots, especially first officers, have been working at below-market rates for years, and under substandard work rules. "